Experimental evidence for the existence of non-nuclear maxima in the electron-density distribution of metallic beryllium. A comparative study of the maximum entropy method and the multipole refinement method.

The electron-density distribution (EDD) of metallic beryllium has been derived from the structure factors of Larsen & Hansen [(1984). Acta Cryst. B40, 169-179] using the maximum entropy method (MEM). Subsequent topological analysis reveals non-nuclear maxima (NNM) in the EDD. Plots of the gradient field of the electron density illustrates this finding. A possible critical-point network for the hexagonal close-packed (h.c.p.) structure of beryllium is suggested. It is thus demonstrated that it is possible to obtain detailed topological information about the electron density in metallic beryllium without the use of a structural model. In order to test the findings of the MEM, the same set of structure factors were analysed using the multipole refinement method (MRM). Use of the MRM also reveals NNM. The results of the two different approaches to electron-density analysis are contrasted and discussed. Expressed within the framework of the theory of atoms in molecules, our results suggest that the h.c.p. structure of beryllium has no Be atoms directly bonded to other Be atoms. The structure is held together through a three-dimensional network of bonds between the NNM and Be atoms as well as between different NNM. The topological analysis thus reveals that the beryllium structure has important interactions connecting Be atoms of different basal plane layers. The breaking of these interactions when forming a surface may explain the abnormally large expansion of the inter-layer distance in the beryllium surface structure.